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Assignment:Find the solution set of inequality 1 <= sqrt(x^2+(2*x-3)^2) <= 3 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
1 <= sqrt ( x ^ 2 + ( 2 * x - 3 ) ^ 2 ) (1)
sqrt ( x ^ 2 + ( 2 * x - 3 ) ^ 2 ) <= 3 (2)
From the definition field of √
x ^ 2 + ( 2 * x - 3 ) ^ 2 ≥ 0 (3 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
0 ≤ x ≤ 12/5
From inequality(3):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequalities (1) and (2)
0 ≤ x ≤ 12/5 (4)
From inequalities (3) and (4)
0 ≤ x ≤ 12/5 (5)
The final solution set is :
0 ≤ x ≤ 12/5Your problem has not been solved here? Please take a look at the hot problems !